Some potential theory of processes with stationary independent increments by means of the Schwartz distribution theory

Takesi WATANABE

doi:10.2969/jmsj/02420213

Takesi WATANABE

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1972 Volume 24 Issue 2 Pages 213-231

DOI https://doi.org/10.2969/jmsj/02420213

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Published: 1972 Received: August 24, 1971 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968.
2) Ph. Courrège, Générateur infinitesimal d'un semi-groupe de convolution sur Rⁿ, et formule de Lévy-Khintchine, Bull. Sci. Math., 88 (1964), 3-30.
3) H. Cramér, Collective Risk Theory, Ab Nordiska Boghandein, Stockholm, 1955.
4) W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, Wiley, New York, 1966.
5) C.S. Herz, Théorie élémentaire des distributions de Beurling, Publication du Séminaire de Mathématiques d'Orsay, 2éme année, 1962/3.
6) G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc., 81 (1956), 264-293.
7) K. Ito, On stochastic differential equations, Mem. Amer. Math. Soc., No. 4(1951).
8) K. Ito, Stochastic Processes II, (in Japanese), Iwanami, Tokyo, 1957. (This book has a Russian translation and an English translation by Y. Ito in a mimeographed version.)
9) K. Sato, Potential operators for Markov processes, to appear.
10) L. Schwartz, Théorie des Distributions, Hermann, Paris, 1966.
11) S. Watanabe, On stable processes with boundary conditions, J. Math. Soc. Japan, 14 (1962), 170-198.
12) T. Watanabe, On balayées of excessive measures and functions with respect to resolvents, 311-341 of Séminaire de Probabilités V, Université de Strasbourg, Lecture Notes in Math. No. 191, Springer, Berlin, 1971.
13) T. Watanabe, An integro-differential equation for a compound Poisson process with drift and the integral equation of H. Cramér, Osaka J. Math., 8 (1971), 377-383.
14) K. Yosida, An operator-theoretical treatment of temporally homogeneous Markoff process, J. Math. Soc. Japan, 1 (1949), 244-253.
15) K. Yosida, Functional Analysis, Springer, Berlin, 1965.

Right : [1] R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968.
[2] Ph. Courrège, Générateur infinitesimal d'un semi-groupe de convolution sur Rⁿ, et formule de Lévy-Khintchine, Bull. Sci. Math., 88 (1964), 3-30.
[3] H. Cramér, Collective Risk Theory, Ab Nordiska Boghandein, Stockholm, 1955.
[4] W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, Wiley, New York, 1966.
[5] C. S. Herz, Théorie élémentaire des distributions de Beurling, Publication du Séminaire de Mathématiques d'Orsay, 2éme année, 1962/3.
[6] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc., 81 (1956), 264-293.
[7] K. Itô, On stochastic differential equations, Mem. Amer. Math. Soc., No. 4 (1951).
[8] K. Itô, Stochastic Processes II, (in Japanese), Iwanami, Tokyo, 1957. (This book has a Russian translation and an English translation by Y. Itô in a mimeographed version.)
[9] K. Sato, Potential operators for Markov processes, to appear.
[10] L. Schwartz, Théorie des Distributions, Hermann, Paris, 1966.
[11] S. Watanabe, On stable processes with boundary conditions, J. Math. Soc. Japan, 14 (1962), 170-198.
[12] T. Watanabe, On balayées of excessive measures and functions with respect to resolvents, 311-341 of Séminaire de Probabilités V, Université de Strasbourg, Lecture Notes in Math. No. 191, Springer, Berlin, 1971.
[13] T. Watanabe, An integro-differential equation for a compound Poisson process with drift and the integral equation of H. Cramér, Osaka J. Math., 8 (1971), 377-383.
[14] K. Yosida, An operator-theoretical treatment of temporally homogeneous Markoff process, J. Math. Soc. Japan, 1 (1949), 244-253.
[15] K. Yosida, Functional Analysis, Springer, Berlin, 1965.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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